Problem on Trigonometric Identity

Trigonometric Identities are the standard equations used to solve trigonometric problems.
Below is as one such problem.

Topic : Trigonometric Identity

A proof for Trigonometric Identity

Problem : Prove the given identity 2 Cos x - 2 Cos³ x = Sin x Sin 2x

Solution :

LHS : 2 Cos x - 2 Cos³ x

= 2 Cos x (1 - Cos²x)
= 2 Cos x . Sin² x
= 2 Cos x . Sin x . Sinx
= Sin x . 2 Sin x Cos x
= Sin x . Sin 2x (using Sin 2x = 2 Sinx Cox x)

So we proved 2 Cos x - 2 Cos³ x = Sin x Sin 2x

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